How many details to include in a chart

This graphic by Bloomberg provides the context for understanding the severity of the Atlantic storm season. (link)

At this point of the season, 2020 appears to be one of the most severe in history.

I was momentarily fascinated by a feature of modern browser-based data visualization: the death of the aspect ratio. When the browser window is stretched sufficiently wide, the chart above is transformed to this look:

The chart designer has lost control of the aspect ratio.

***

This Bloomberg chart is an example of the spaghetti-style plots that convey variability by displaying individual units of data (here, storm years). The envelope of the growth curves gives the range of historical counts while the density of curves roughly offers some sense of the most likely counts at different points of the season.

But these spaghetti-style plots are not precise at conveying the variability because the density is hard to gauge. That's where aggregating the individual units helps.

The following chart does not show individual storm years. It shows the counts for the median season at selected points in time, and also a band of variability (for example, you'd include say 90 or 95% of the seasons).

I don't have the raw data so the aggregating is done by eyeballing the spaghetti.

I prefer this presentation even though it does not plot every single data point one has in the dataset.

 

 

On data volume, reliability, uncertainty and confidence bands

This chart from the Economist caught my eye because of the unusual use of color-coded hexagonal tiles.

The basic design of the chart is easy to grasp: It relates people's "happiness" to national wealth. The thick black line shows that the average citizen of wealthier countries tends to rate their current life situation better.

For readers alert to graphical details, things can get a little confusing. The horizontal "wealth" axis is shown in log scale, which means that the data on the right side of the chart have been compressed while the data on the left side of the chart have been stretched out. In other words, the curve in linear scale is much flatter than depicted.

One thing you might notice is how poor the fit of the line is at both ends. Singapore and Afghanistan are clearly not explained by the fitted line. (That said, the line is based on many more dots than those eight we can see.) Moreover, because countries are widely spread out on the high end of the wealth axis, the fit is not impressive. Log scales tend to give a false impression of the tightness of fit, as I explained before when discussing coronavirus case curves.

***

The hexagonal tiles replace the more typical dot scatter or contour shading. The raw data consist of results from polls conducted in different countries in different years. For each poll, the analyst computes the average life satisfaction score for that country in that year. From national statistics, the analyst pulls out that country's GDP per capita in that year. Thus, each data point is a dot on the canvass. A few data points are shown as black dots. Those are for eight highlighted countries for the year 2018.

The black line is fitted to the underlying dot scatter and summarizes the correlation between average wealth and average life satisfaction. Instead of showing the scatter, this Economist design aggregates nearby dots into hexagons. The deepest red hexagon, sandwiched between Finland and the US, contains about 60-70 dots, according to the color legend.

These details are tough to take in. It's not clear which dots have been collected into that hexagon: are they all Finland or the U.S. in various years, or do they include other countries? Each country is represented by multiple dots, one for each poll year. It's also not clear how much variation there exists within a country across years.

***

The hexagonal tiles presumably serve the same role as a dot scatter or contour shading. They convey the amount of data supporting the fitted curve along its trajectory. More data confers more reliability.

For this chart, the hexagonal tiles do not add any value. The deepest red regions are those closest to the black line so nothing is actually lost by showing just the line and not the tiles.

Using the line chart obviates the need for readers to figure out the hexagons, the polls, the aggregation, and the inevitable unanswered questions.

***

An alternative concept is to show the "confidence band" or "error bar" around the black line. These bars display the uncertainty of the data. The wider the band, the less certain the analyst is of the estimate. Typically, the band expands near the edges where we have less data.

Here is conceptually what we should see (I don't have the underlying dataset so can't compute the confidence band precisely)

The confidence band picture is the mirror image of the hexagonal tiles. Where the poll density is high, the confidence band narrows, and where poll density is low, the band expands.

A simple way to interpret the confidence band is to find the country's wealth on the horizontal axis, and look at the range of life satisfaction rating for that value of wealth. Now pick any number between the range, and imagine that you've just conducted a survey and computed the average rating. That number you picked is a possible survey result, and thus a valid value. (For those who know some probability, you should pick a number not at random within the range but in accordance with a Bell curve, meaning picking a number closer to the fitted line with much higher probability than a number at either edge.)

Visualizing data involves a series of choices. For this dataset, one such choice is displaying data density or uncertainty or neither.

This chart shows why the PR agency for the UK government deserves a Covid-19 bonus

The Economist illustrated some interesting consumer research with this chart (link):

The survey by Dalia Research asked people about the satisfaction with their country's response to the coronavirus crisis. The results are reduced to the "Top 2 Boxes", the proportion of people who rated their government response as "very well" or "somewhat well".

This dimension is laid out along the horizontal axis. The chart is a combo dot and bubble chart, arranged in rows by region of the world. Now what does the bubble size indicate?

It took me a while to find the legend as I was expecting it either in the header or the footer of the graphic. A larger bubble depicts a higher cumulative number of deaths up to June 15, 2020.

The key issue is the correlation between a country's death count and the people's evaluation of the government response.

Bivariate correlation is typically shown on a scatter plot. The following chart sets out the scatter plots in a small multiples format with each panel displaying a region of the world.

The death tolls in the Asian countries are low relative to the other regions, and yet the people's ratings vary widely. In particular, the Japanese people are pretty hard on their government.

In Europe, the people of Greece, Netherlands and Germany think highly of their government responses, which have suppressed deaths. The French, Spaniards and Italians are understandably unhappy. The British appears to be the most forgiving of their government, despite suffering a higher death toll than France, Spain or Italy. This speaks well of their PR operation.

Cumulative deaths should be adjusted by population size for a proper comparison across nations. When the same graphic is produced using deaths per million (shown on the right below), the general story is preserved while the pattern is clarified:

The right chart shows deaths per million while the left chart shows total deaths.

***

In the original Economist chart, what catches our attention first is the bubble size. Eventually, we notice the horizontal positioning of these bubbles. But the star of this chart ought to be the new survey data. I swapped those variables and obtained the following graphic:

Instead of using bubble size, I switched to using color to illustrate the deaths-per-million metric. If ratings of the pandemic response correlate tightly with deaths per million, then we expect the color of these dots to evolve from blue on the left side to red on the right side.

The peculiar loss of correlation in the U.K. stands out. Their PR firm deserves a bonus!

Cornell must remove the logs before it reopens the campus in the fall

Against all logic, Cornell announced last week it would re-open in the fall because a mathematical model under development by several faculty members and grad students predicts that a "full re-opening" would lead to 80 percent fewer infections than a scenario of full virtual instruction. That's what was reported by the media.

The model is complicated, with loads of assumptions, and the report is over 50 pages long. I will put up my notes on how they attained this counterintuitive result in the next few days. The bottom line is - and the research team would agree - it is misleading to describe the analysis as "full re-open" versus "no re-open". The so-called full re-open scenario assumes the entire community including students, faculty and staff submit to a full program of test-trace-isolate, including (mandatory) PCR diagnostic testing once every five days throughout the 16-week semester, and immediate quarantine and isolation of new positive cases, as well as those in contact with such persons, plus full compliance with this program. By contrast, it assumes students do not get tested in the online instruction scenario. In other words, the researchers expect Cornell to get done what the U.S. governments at all levels failed to do until now.

[7/8/2020: The post on the Cornell model is now up on the book blog. Here.]

The report takes us back to the good old days of best-base-worst-case analysis. There is no data for validating such predictions so they performed sensitivity analyses, defined as changing one factor at a time assuming all other factors are fixed at "nominal" (i.e. base case) values. In a large section of the report, they publish a series of charts of the following style:

Each line here represents one of the best-base-worst cases (respectively, orange-blue-green). Every parameter except one is given the "nominal" value (which represents the base case). The parameter that is manpulated is shown on the horizontal axis, and for the above chart, the variable is the assumption of average number of daily contacts per person. The vertical axis shows the main outcome variable, which is the percentage of the community infected by the end of term.

This flatness of the lines in the above chart appears to say that the outcome is quite insensitive to the change in the average daily contact rate under all three scenarios - until the daily contact rises above 10 per person per day. It also appears to show that the blue line is roughly midway between the orange and the green so the percent infected is slightly less-than halved under the optimistic scenario, and a bit more than doubled under the pessimistic scenario, relative to the blue line.

Look again.

The vertical axis is presented in log scale, and only labeled at values 1% and 10%. About midway between 1 and 10 on the horizontal axis, the outcome value has already risen above 10%. Because of the log transformation, above 10%, each tick represents an increase of 10% in proportion. So, the top of the vertical axis indicates 80% of the community being infected! Nothing in the description or labeling of the vertical axis prepares the reader for this.

The report assumes a fixed value for average daily contacts of 8 (I rounded the number for discussion), which is invariable across all three scenarios. Drawing a vertical line about eight-tenths of the way towards 10 appears to signal that this baseline daily contact rate places the outcome in the relatively flat part of the curve.

Look again.

The horizontal axis too is presented in log scale. To birth one log-scale may be regarded as a misfortune; to birth two log scales looks like carelessness. 

Since there exists exactly one tick beyond 10 on the horizontal axis, the right-most value is 20. The model has been run for values of average daily contacts from 1 to 20, with unit increases. I can think of no defensible reason why such a set of numbers should be expressed in a log scale.

For the vertical axis, the outcome is a proportion, which is confined to within 0 percent and 100 percent. It's not a number that can explode.

***

Every log scale on a chart is birthed by its designer. I know of no software that automatically performs log transforms on data without the user's direction. (I write this line with trepidation wishing that I haven't planted a bad idea in some software developer's head.)

Here is what the shape of the original data looks like - without any transformation. All software (I'm using JMP here) produces something of this type:

At the baseline daily contact rate value of 8, the model predicts that 3.5% of the Cornell community will get infected by the end of the semester (again, assuming strict test-trace-isolate fully implemented and complied).  Under the pessimistic scenario, the proportion jumps to 14%, which is 4 or 5 times higher than the base case. In this worst-case scenario, if the daily contact rate were about twice the assumed value (just over 16), half of the community would be infected in 16 weeks!

I actually do not understand how there could only be 8 contacts per person per day when the entire student body has returned to 100% in-person instruction. (In the report, they even say the 8 contacts could include multiple contacts with the same person.) I imagine an undergrad student in a single classroom with 50 students. This assumption says the average student in this class only comes into contact with at most 8 of those. That's one class. How about other classes? small tutorials? dining halls? dorms? extracurricular activities? sports? parties? bars?

Back to graphics. Something about the canonical chart irked the report writers so they decided to try a log scale. Here is the same chart with the vertical axis in log scale:

The log transform produces a visual distortion. On the right side, where the three lines are diverging rapidly, the log transform pulls them together. On the left side, where the three lines are close together, the log transform pulls them apart.

Recall that on the log scale, a straight line is exponential growth. Look at the green line (worst case). That line is approximately linear so in the pessimistic scenario, despite assuming full compliance to a strict test-trace-isolate regimen, the cases are projected to grow exponentially.

Something about that last chart still irked the report writers so they decided to birth a second log scale. Here is the chart they ultimately settled on:

As with the other axis, the effect of the log transform is to squeeze the larger values (on the right side) and spread out the smaller values (on the left side). After this cosmetic surgery, the left side looks relatively flat while the right side looks steep.

In the next version of the Cornell report, they should replace all these charts with ones using linear scales.

***

Upon discovering this graphical mischief, I wonder if the research team received a mandate that includes a desired outcome.

 

[P.S. 7/8/2020. For more on the Cornell model, see this post.]

What is the price for objectivity

I knew I had to remake this chart.

The simple message of this chart is hidden behind layers of visual complexity. What the analyst wants readers to focus on (as discerned from the text on the right) is the red line, the seven-day moving average of new hospital admissions due to Covid-19 in Texas.

My eyes kept wandering away from the line. It's the sideway data labels on the columns. It's the columns that take up vastly more space than the red line. It's the sideway date labels on the horizontal axis. It's the redundant axis labels for hospitalizations when the entire data set has already been printed. It's the two hanging diamonds, for which the clues are filed away in the legend above.

Here's a version that brings out the message: after Phase 2 re-opening, the number of hospital admissions has been rising steadily.

Dots are used in place of columns, which push these details to the background. The line as well as periods of re-opening are directly labeled, removing the need for a legend.

Here's another visualization:

This chart plots the weekly average new hospital admissions, instead of the seven-day moving average. In the previous chart, the raggedness of moving average isn't transmitting any useful information to the average reader. I believe this weekly average metric is easier to grasp for many readers while retaining the general story.

***

On the original chart by TMC, the author said "the daily hospitalization trend shows an objective view of how COVID-19 impacts hospital systems." Objectivity is an impossible standard for any kind of data analysis or visualization. As seen above, the two metrics for measuring the trend in hospitalizations have pros and cons. Even if one insists on using a moving average, there are choices of averaging methods and window sizes.

Scientists are trained to believe in objectivity. It frequently disappoints when we discover that the rest of the world harbors no such notion. If you observe debates between politicians or businesspeople or social scientists, you rarely hear anyone claim one analysis is more objective - or less subjective - than another. The economist who predicts Dow to reach a new record, the business manager who argues for placing discounted products in the front not the back of the store, the sportscaster who maintains Messi is a better player than Ronaldo: do you ever hear these people describe their methods as objective?

Pursuing objectivity leads to the glorification of data dumps. The scientist proclaims disinterest in holding an opinion about the data. This is self-deception though. We clearly have opinions because when someone else  "misinterprets" the data, we express dismay. What is the point of pretending to hold no opinions when most of the world trades in opinions? By being "objective," we never shape the conversation, and forever play defense.

Designs of two variables: map, dot plot, line chart, table

The New York Times found evidence that the richest segments of New Yorkers, presumably those with second or multiple homes, have exited the Big Apple during the early months of the pandemic. The article (link) is amply assisted by a variety of data graphics.

The first few charts represent different attempts to express the headline message. Their appearance in the same article allows us to assess the relative merits of different chart forms.

First up is the always-popular map.

The advantage of a map is its ease of comprehension. We can immediately see which neighborhoods experienced the greater exoduses. Clearly, Manhattan has cleared out a lot more than outer boroughs.

The limitation of the map is also in view. With the color gradient dedicated to the proportions of residents gone on May 1st, there isn't room to express which neighborhoods are richer. We have to rely on outside knowledge to make the correlation ourselves.

The second attempt is a dot plot.

We may have to take a moment to digest the horizontal axis. It's not time moving left to right but income percentiles. The poorest neighborhoods are to the left and the richest to the right. I'm assuming that these percentiles describe the distribution of median incomes in neighborhoods. Typically, when we see income percentiles, they are based on households, regardless of neighborhoods. (The former are equal-sized segments, unlike the latter.)

This data graphic has the reverse features of the map. It does a great job correlating the drop in proportion of residents at home with the income distribution but it does not convey any spatial information. The message is clear: The residents in the top 10% of New York neighborhoods are much more likely to have left town.

In the following chart, I attempted a different labeling of both axes. It cuts out the need for readers to reverse being home to not being home, and 90th percentile to top 10%.

The third attempt to convey the income--exit relationship is the most successful in my mind. This is a line chart, with time on the horizontal axis.

The addition of lines relegates the dots to the background. The lines show the trend more clearly. If directly translated from the dot plot, this line chart should have 100 lines, one for each percentile. However, the closeness of the top two lines suggests that no meaningful difference in behavior exists between the 20th and 80th percentiles. This can be conveyed to readers through a short note. Instead of displaying all 100 percentiles, the line chart selectively includes only the 99th , 95th, 90th, 80th and 20th percentiles. This is a design choice that adds by subtraction.

Along the time axis, the line chart provides more granularity than either the map or the dot plot. The exit occurred roughly over the last two weeks of March and the first week of April. The start coincided with New York's stay-at-home advisory.

This third chart is a statistical graphic. It does not bring out the raw data but features aggregated and smoothed data designed to reveal a key message.

I encourage you to also study the annotated table later in the article. It shows the power of a well-designed table.

[P.S. 6/4/2020. On the book blog, I have just published a post about the underlying surveillance data for this type of analysis.]

 

 

Hope and reality in one Georgia chart

Over the weekend, Georgia's State Health Department agitated a lot of people when it published the following chart:

(This might have appeared a week ago as the last date on the chart is May 9 and the title refers to "past 15 days".)

They could have avoided the embarrassment if they had read my article at DataJournalism.com (link). In that article, I lay out a set of the "unspoken conventions," things that visual designers are, or should be, doing more or less in their sleep. Under the section titled "Order", I explain the following two "rules":

• Place values in the natural order when it is available
• Retain the same order across all plots in a panel of charts

In the chart above, the natural order for the horizontal (time) axis is time running left to right. The order chosen by the designer  is roughly but not precisely decreasing height of the tallest column in each daily group. Many observers suggested that the columns were arranged to give the appearance of cases dropping over time.

Within each day, the counties are ordered in decreasing number of new cases. The title of the chart reads "number of cases over time" which sounds like cumulative cases but it's not. The "lead" changed hands so many times over the 15 days, meaning the data sequence was extremely noisy, which would be unlikely for cumulative cases. There are thousands of cases in each of these counties by May. Switching the order of the columns within each daily group defeats the purpose of placing these groups side-by-side.

Responding to the bad press, the department changed the chart design for this week's version:

This chart now conforms to the two spoken rules described above. The time axis runs left to right, and within each group of columns, the order of the counties is maintained.

The chart is still very noisy, with no apparent message.

***

Next, I'd like to draw your attention to a Data issue. Notice that the 15-day window has shifted. This revised chart runs from May 2 to May 16, which is this past Saturday. The previous chart ran from Apr 26 to May 9. 

Here's the data for May 8 and 9 placed side by side.

There is a clear time lag of reporting cases in the State of Georgia. This chart should always exclude the last few days. The case counts keep going up until it stabilizes. The same mistake occurs in the revised chart - the last two days appear as if new cases have dwindled toward zero when in fact, it reflects a lag in reporting.

The disconnect between the Question being posed and the quality of the Data available dooms this visualization. It is not possible to provide a reliable assessment of the "past 15 days" when during perhaps half of that period, the cases are under-counted.

***

This graphical distortion due to "immature" data has become very commonplace in Covid-19 graphics. It's similar to placing partial-year data next to full-year results, without calling out the partial data.

The following post from the ancient past (2005!) about a New York Times graphic shows that calling out this data problem does not actually solve it. It's a less-bad kind of thing.

The coronavirus data present more headaches for graphic designers than the financial statistics. Because of accounting regulations, we know that only the current quarter's data are immature. For Covid-19 reporting, the numbers are being adjusted for days and weeks.

Practically all immature counts are under-estimates. Over time, more cases are reported. Thus, any plots over time - if unadjusted - paint a misleading picture of declining counts. The effect of the reporting lag is predictable, having a larger impact as we run from left to right in time. Thus, even if the most recent data show a downward trend, it can eventually mean anything: down, flat or up. This is not random noise though - we know for certain of the downward bias; we just don't know the magnitude of the distortion for a while.

Another issue that concerns coronavirus reporting but not financial reporting is inconsistent standards across counties. Within a business, if one were to break out statistics by county, the analysts would naturally apply the same counting rules. For Covid-19 data, each county follows its own set of rules, not just  how to count things but also how to conduct testing, and so on.

Finally, with the politics of re-opening, I find it hard to trust the data. Reported cases are human-driven data - by changing the number of tests, by testing different mixes of people, by delaying reporting, by timing the revision of older data, by explicit manipulation, ...., the numbers can be tortured into any shape. That's why it is extremely important that the bean-counters are civil servants, and that politicians are kept away. In the current political environment, that separation between politics and statistics has been breached.

***

Why do we have low-quality data? Human decisions, frequently political decisions, adulterate the data. Epidemiologists are then forced to use the bad data, because that's what they have. Bad data lead to bad predictions and bad decisions, or if the scientists account for the low quality, predictions with high levels of uncertainty. Then, the politicians complain that predictions are wrong, or too wide-ranging to be useful. If they really cared about those predictions, they could start by being more transparent about reporting and more proactive at discovering and removing bad accounting practices. The fact that they aren't focused on improving the data gives the game away. Here's a recent post on the politics of data.

 

How Covid-19 deaths sneaked into Florida's statistics

Like many others, some Floridians are questioning their state's Covid statistics. It's clear there are numerous "degrees of freedom" for politicians to manipulate the numbers. What's not clear is who's influencing these decisions. Are they public-health experts, donors, voters, or whom?

A Twitter follower sent in the following chart, embedded in an informative article in Sun-Sentinel:

I like the visual design. It's clean, and conveys a moderately complex concept effectively. The reader may not immediately get what metrics are being plotted but the idea that the blue line should operate within the gray area.. until it doesn't is easily grasped. The range is technically an uncertainty band.

The metric is the proportion of total deaths (all causes) that are attributed to pneumonia and flu. Typical influenza deaths are found in that category. This chart investigates whether there were excess (unexplained) P&F deaths. The gray band measures the variability in the proportions of past years. When the blue line operates inside the band, the metric is normal. When it pierces the upper band, which happened here around week 25, a rare event has occurred.

The concern on Twitter was about the horizontal axis. Those integer labels can be confusing. The designer places a "how to read this" message in a footnote, explaining that week 1 is the first week of a typical flu season (which corresponds to late September 2019). This nugget of information helps a lot. We can see that the flu season peaks around week 20, and by the spring, it should be waning. Not so in 2020.

It's hard to escape the conclusion that deaths from Covid-19 are hiding inside the statistics of Pneumonia & Flu. As a statistician, I want to tell you Statistics Don't Lie! You can hide the data along one dimension, but they show up elsewhere. Misclassifying the deaths does buy someone some time. It takes a few weeks to compile all-cause mortality data (gasp, the CDC said mortality records are only 75 percent accurate after 8 weeks!)

The other small problem with the chart is the labeling. Neither axis has labels. The data label that shows up when you click on the line might be a default from the software that can't be turned off. It shows the two numbers being plotted without labels.

***

Here is a re-working of the chart that tells the story:

The proportion of deaths attributed to P&F and Covid together is roughly double the upper end of what Florida should be seeing this time of the year (without Covid). Covid-19 accounts for half the gap. The other half are still being classified as P&F. However, I suspect CDC will adjust these numbers later to reflect the reality. (In making this chart, I also learned that Florida stopped including seasonal visitors in the death counts. This is egregious manipulation. If someone died while in Florida, they should be counted. I didn't investigate whether this counting rule applies only to Covid-19 deaths, or to deaths from all causes. If they had always done that, then I might give them a pass.)

On second thought, maybe not. The other egregious thing that appeared to have happened is that the Florida state health department unplugged their prior website (https://www.floridahealth.gov) so no one can cross-reference any prior documents. The only website I can access now for Florida state health is a Covid-specific site (https://floridahealthcovid19.gov).

There must be something juicy on the previous influenza page, no?

***

Lastly, when you look at my chart, please pretend that the last week is not on there. In all likelihood, the "drop" is fake because the mortality data have not been fully updated. My chart contains one more week than the Sun Sentinel chart. So you can see that the drastic decline shown on their chart turned up a big uptick on mine (next to last week).

This is a common mistake on many charts I see these days. Half-baked numbers are shown next to fully-baked ones.

Twitter people UpSet with that Covid symptoms diagram

Been busy with an exciting project, which I might talk about one day. But I promised some people I'll follow up on Covid symptoms data visualization, so here it is.

After I posted about the Venn diagram used to depict self-reported Covid-19 symptoms by users of the Covid Symptom Tracker app (reported by Nature), Xan and a few others alerted me to Twitter discussion about alternative visualizations that people have made after they suffered the indignity of trying to parse the Venn diagram.

To avoid triggering post-trauma, for those want to view the Venn diagram, please click here.

[In the Twitter links below, you almost always have to scroll one message down - saving tweets, linking to tweets, etc. are all stuff I haven't fully figured out.]

Start with the Questions

Xan’s final comment is especially appropriate: "There's an over-riding Type-Q issue: count charts answer the wrong question".

As dataviz designers, we frequently get locked into the mindset of “what is the best way to present this dataset?” This line of thinking leads to overloaded graphics that attempt to answer every possible question that may arise from the data in one panoptic chart, akin to juggling 10 balls at once.

For complex datasets, it is often helpful to narrow down the list of questions, and provide a series of charts, each addressing one or two questions. I’ll come back to this point. I want to first show some of the nicer visuals that others have produced, which brings out the structure and complexity of this dataset.

 

The UpSet chart

The primary contender is the “UpSet” chart form, as best exemplified by Bart’s effort

The centerpiece of this chart is the matrix of dots. The horizontal rows of dots represent the presence of specific symptoms such as cough and anosmia (loss of smell and taste). The vertical columns are intuitive, once you get it. They represent combinations of symptoms, and the fill/no-fill of the dots indicates which symptoms are being combined. For example, the first column counts people reporting fatigue plus anosmia (but nothing else).

The UpSet chart clearly communicates the structure of the data. In many survey questions (including this one conducted by the Symptom Tracker app), respondents are allowed to check/tick more than one answer choices. This creates a situation where the number of answers (here, symptoms) per respondent can be zero up to the total number of answer choices.

So far, we have built a structure like we have drawn country outlines on a map. There is no data yet. The data are primarily found in the sidebar histograms (column/bar charts). Reading horizontally to the right side, one learns that the most frequently reported symptom was fatigue, covering 88 percent of the users.* Reading vertically, one learns that the top combination of symptoms was fatigue plus anosmia, covering 16 percent of users.

***

Now come the divisive acts.

Act 1: Bart orders the columns in a particular way that meets his subjective view of how he wants readers to see the data. The columns are sorted from the most frequent combinations to the least. The histogram has a “long tail”, with most of the combinations receiving a small proportion of the total. The top five combinations is where the bulk of the data is – I’d have liked to see all five columns labeled, without decimal places.

This is a choice on the part of the designer. Nils, for example, made two versions of his UpSet charts. The second version arranges the combinations from singles to quintuples.

 

Digression: The Visual in Data Visualization

The two rendering of “UpSet” charts, by Nils and Bart, is a perfect illustration of the Trifecta Checkup framework. Each corner of the Trifecta is an independent dimension, and yet all must sync. With the same data and the same question types, what differentiates the two versions is the visual design.

See how many differences you can find, and make your own design choices!

 

I place the digression here because Act 1 above has to do with the Q corner, and both visual designs can accommodate the sorting decisions. But Act 2 below pertains to the V corner.

Act 2: Bart applies a blue gradient to the matrix of dots that reinforces his subjective view about identifying frequent combinations of symptoms. Nils, by contrast, uses the matrix to show present/absent only.

I’m not sure about Act 2. I think the addition of the color gradient overloads the matrix in the chart. It has the nice effect of focusing the reader’s attention on the top 5 combinations but it also requires the reader to have understood the meaning of columns first. Perhaps applying the gradient to the histogram up top rather than the dots in the matrix can achieve the same goal with less confusion.

 

Getting Obtuse

For example, some readers (e.g. Robin) expressed confusion.

Robin is alleging something the chart doesn’t do. He pointed out (correctly) that while 16 percent experienced fatigue and anosmia only (without other symptoms), more than 50 percent reported fatigue and anosmia, plus other symptoms. That nugget of information is deeply buried inside Bart’s chart – it’s the sum of each column for which the first two dots are filled in. For example, the second column represents fatigue+anosmia+cough. So Robin wants to aggregate those up.

Robin’s critique arises from the Q(uestion) corner. If the designer wants to highlight specific combinations that occur most frequently in the data, then Bart’s encoding makes perfect sense. On the other hand, if the purpose is to highlight pairs of symptoms that occur most frequently together (disregarding symptoms outside each pair), then the data must be further aggregated. The switch in the Question requires more Data manipulation, which then affects the Visualization. That's the essence of the Trifecta Checkup framework.

Rest assured, the version that addresses Robin’s point will not give an easy answer to Bart’s question. In fact, Xan whipped up a bar chart in response:

This is actually hard to comprehend because Robin’s question is even hard to state. The first bar shows 87 percent of users reported fatigue as a symptom, the same number that appeared on Bart’s version on the right side. Then, the darkened section of the bar indicates the proportion of users who reported only fatigue and nothing else, which appears to be about 10 percent. So 1 out of 9 reported just fatigue while 8 out of 9 who reported fatigue also experienced other symptoms.

 

Xan’s bar chart can be flipped 90 degrees and replace Bart’s histogram on top of the matrix. But you see, we end up with the same problem as I mentioned up top. By jamming more insights from more questions onto the same chart, we risk dropping the other balls that were already in the air.

So, my advice is always to first winnow down the list of questions you want to address. And don’t be afraid of making a series of charts instead of one panoptic chart.

***

Act 3: Bart decides to leave out labels for the columns.

This is a curious choice given the key storyline we’ve been working with so far (the Top 5 combinations of symptoms). But notice how annoying this problem is. Combinations require long text, which must be written vertically or slanted on this design. Transposing could help but not really. It’s just a limitation of this chart form. For me, reading the filled dots underneath the columns as column labels isn’t a show-stopper.

 

Histograms vs Bar Charts

It’s worth pointing out that the sidebar “histograms” are not both histograms. I tend to think of histograms as a specific type of bar (column) chart, in which the sum of the bars (columns) can be interpreted as a whole. So all histograms are bar charts but only some bar charts are histograms.

The column chart up top is a histogram. The combinations of symptoms are disjoint, and the total of the combinations should be the total number of answer choices selected by all respondents. The bar chart on the right side however is not a histogram. Each percentage is a proportion to the whole, and adding those percentages yields way above 100%.

I like the annotation on Bart’s chart a lot. They are succinct and they give just the right information to explain how to read the chart.

 

Limitations

I already mentioned the vertical labeling issue for UpSet charts. Here are two other considerations for you.

The majority of the plotting area is dedicated to the matrix of dots. The matrix contains merely labels for data. They are like country boundaries on a map. While it lays out the structure of data very clearly, the designer should ask whether it is essential for the readers to see the entire landscape.

In real-world data, the “long tail” phenomenon we saw earlier is very common. With six featured symptoms, there are 2^6 = 64 possible combinations of symptoms (minus 1 if they filtered out those not reporting symptoms*), almost all of which will be empty. Should the low-frequency columns be removed? This is not as controversial as you think, because implicitly both Bart and Nils already dropped all empty combinations!

 

Data and Code

Kieran Healy left a comment on the last post, and you can find both the data (thank you!) and some R code for UpSet charts at his blog.

Also, Nils has a Shiny app on Github.

 

(*) One must be very careful about what “users” are being represented. They form a tiny subset of users of the Symptom Tracker app, just those who have previously taken a diagnostic test and have self-reported at least one symptom. I have separately commented on the analyses of this dataset by the team behind the app. The first post discusses their analytical methods, the second post examines how they pre-processed the data, and a future post will describe the data collection practices. For the purpose of this blog post, I’ll ignore any data issues.

(#) Bart’s chart is conceptual because some of the columns of dots are repeated, and there is one column without fills, which should have been removed by a pre-processing step applied by the research team.

Reviewing the charts in the Oxford Covid-19 study

On my sister (book) blog, I published a mega-post that examines the Oxford study that was cited two weeks ago as a counterpoint to the "doomsday" Imperial College model. These studies bring attention to the art of statistical modeling, and those six posts together are designed to give you a primer, and you don't need math to get a feel.

One aspect that didn't make it to the mega-post is the data visualization. Sad to say, the charts in the Oxford study (link) are uniformly terrible. Figure 3 is typical:

There are numerous design decisions that frustrate readers.

a) The graphic contains two charts, one on top of the other. The left axis extends floor-to-ceiling, giving the false impression that it is relevant to both charts. In fact, the graphic uses dual axes. The bottom chart references the axis shown in the bottom right corner; the left axis is meaningless. The two charts should be drawn separately.

For those who have not read the mega-post about the Oxford models, let me give a brief description of what these charts are saying. The four colors refer to four different models - these models have the same structure but different settings. The top chart shows the proportion of the population that is still susceptible to infection by a certain date. In these models, no one can get re-infected, and so you see downward curves. The bottom chart displays the growth in deaths due to Covid-19. The first death in the UK was reported on March 5.  The black dots are the official fatalities.

b) The designer allocates two-thirds of the space to the top chart, which has a much simpler message. This causes the bottom chart to be compressed beyond cognition.

c) The top chart contains just five lines, smooth curves of the same shape but different slopes. The designer chose to use thick colored lines with black outlines. As a result, nothing precise can be read from the chart. When does the yellow line start dipping? When do the two orange lines start to separate?

d) The top chart should have included margins of error. These models are very imprecise due to the sparsity of data.

e) The bottom chart should be rejected by peer reviewers. We are supposed to judge how well each of the five models fits the cumulative death counts. But three design decisions conspire to prevent us from getting the answer: (i) the vertical axis is severely compressed by tucking this chart underneath the top chart (ii) the vertical axis uses a log scale which compresses large values and (iii) the larger-than-life dots.

As I demonstrated in this post also from the sister blog, many models especially those assuming an exponential growth rate has poor fits after the first few days. Charting in log scale hides the degree of error.

f) There is a third chart squeezed into the same canvass. Notice the four little overlapping hills located around Feb 1. These hills are probability distributions, which are presented without an appropriate vertical axis. Each hill represents a particular model's estimate of the date on which the novel coronavirus entered the UK. But that date is unknowable. So the model expresses this uncertainty using a probability distribution. The "peak" of the distribution is the most likely date. The spread of the hill gives the range of plausible dates, and the height at a given date indicates the chance that that is the date of introduction. The missing axis is a probability scale, which is neither the left nor the right axis.

***

The bottom chart shows up in a slightly different form as Figure 1(A).

Here, the green, gray (blocked) and red thick lines correspond to the yellow/orange/red diamonds in Figure 3. The thin green and red lines show the margins of error I referred to above (these lines are not explicitly explained in the chart annotation.) The actual counts are shown as white rather than black diamonds.

Again, the thick lines and big diamonds conspire to swamp the gaps between model fit and actual data. Again, notice the use of a log scale. This means that the same amount of gap signifies much bigger errors as time moves to the right.

When using the log scale, we should label it using the original units. With a base 10 logarithm, the axis should have labels 1, 10, 100, 1000 instead of 0, 1, 2, 3. (This explains my previous point - why small gaps between a model line and a diamond can mean a big error as the counts go up.)

Also notice how the line of white diamonds makes it impossible to see what the models are doing prior to March 5, the date of the first reported death. The models apparently start showing fatalities prior to March 5. This is a key part of their conclusion - the Oxford team concluded that the coronavirus has been circulating in the U.K. even before the first infection was reported. The data visualization should therefore bring out the difference in timing.

I hope by the time the preprint is revised, the authors will have improved the data visualization.